Answer :
To write the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] in descending order, we need to arrange the terms starting with the highest power of [tex]\(x\)[/tex] and proceed to the lowest. Here's how you can do it step-by-step:
1. Identify the Terms and their Exponents:
- [tex]\(4x^{12}\)[/tex]: The exponent is 12.
- [tex]\(9x^7\)[/tex]: The exponent is 7.
- [tex]\(3x^3\)[/tex]: The exponent is 3.
- [tex]\(-x\)[/tex] is equivalent to [tex]\(-1x^1\)[/tex]: The exponent is 1.
2. Arrange the Terms by Exponents in Descending Order:
- First term: The largest exponent is 12, so [tex]\(4x^{12}\)[/tex] comes first.
- Second term: The next largest exponent is 7, so [tex]\(9x^7\)[/tex] comes next.
- Third term: Then comes [tex]\(3x^3\)[/tex] with an exponent of 3.
- Fourth term: Finally, [tex]\(-x\)[/tex] (or [tex]\(-1x^1\)[/tex]) has the smallest exponent, 1.
3. Write the Polynomial with Terms in Descending Order of Exponents:
- Collect the arranged terms: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
Thus, the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] written in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
The correct choice from the given options is:
D. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
1. Identify the Terms and their Exponents:
- [tex]\(4x^{12}\)[/tex]: The exponent is 12.
- [tex]\(9x^7\)[/tex]: The exponent is 7.
- [tex]\(3x^3\)[/tex]: The exponent is 3.
- [tex]\(-x\)[/tex] is equivalent to [tex]\(-1x^1\)[/tex]: The exponent is 1.
2. Arrange the Terms by Exponents in Descending Order:
- First term: The largest exponent is 12, so [tex]\(4x^{12}\)[/tex] comes first.
- Second term: The next largest exponent is 7, so [tex]\(9x^7\)[/tex] comes next.
- Third term: Then comes [tex]\(3x^3\)[/tex] with an exponent of 3.
- Fourth term: Finally, [tex]\(-x\)[/tex] (or [tex]\(-1x^1\)[/tex]) has the smallest exponent, 1.
3. Write the Polynomial with Terms in Descending Order of Exponents:
- Collect the arranged terms: [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
Thus, the polynomial [tex]\(3x^3 + 9x^7 - x + 4x^{12}\)[/tex] written in descending order is [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex].
The correct choice from the given options is:
D. [tex]\(4x^{12} + 9x^7 + 3x^3 - x\)[/tex]
